Visiting the Texas town of Laredo for a "boots on the ground" trip, the Republican hopeful said the United States faces "a tremendous danger on the border with the illegals coming in".

Asked whether he had evidence for his claim that Mexico sends rapists and other criminals across the border, he replied, "Yes, I have, and I've heard it from a lot of different people."

Trump is at, or near, the top of many opinion polls among the 16 candidates in the race for the Republican nomination for the 2016 presidential election, worrying leaders in the party establishment who fear he could turn off moderate voters.

Trump's Texas trip started badly when Border Patrol agents who had been scheduled to accompany him pulled out at the last minute.

"They were totally silenced directly from superiors in Washington who do not want people to know how bad it is on the border, every bit as bad as Mr. Trump has been saying," a Trump statement said.

A spokesman for the national office of the agents' union was not immediately available for comment.

Even as immigration remains a hot topic, the number of people emigrating from Mexico to the United States, legally and illegally, peaked in 2003 and has fallen by more than half since then, according to research published on Wednesday by the University of New Hampshire.

Trump's immigration stance has angered the Mexican government and Hispanics in the United States, but the billionaire said Latino voters "are going to love Trump" because he will win back American jobs from China and Japan.

His suggestion before visiting Laredo that the area is dangerous brought a rebuke from local Democratic State Senator Judith Zafferini.

"Contrary to Trump's vitriolic rhetoric, the border is not a dangerous war zone," she said. "Laredo and El Paso have been ranked among the safest cities in the country, and most border communities' crime rates are equal to, or lower than, the state and national averages."

Trump has been criticized by the Republican establishment for comments about immigration, U.S. Senator John McCain's war record and for personal attacks against fellow Republican White House contenders.

He threatened in an interview published on Thursday to run as a political independent if he does not get "fair" treatment from the Republican Party.